In the way you have said the question it is better to use the word watch than see.

They're both interchangeable in spoken English. But there'a difference in meaning if you are using English more formally: as the other comments show, "watch" is a more active action, where you are paying attention, while "see" is a more passive action.

They are completely interchangeable in this setting. In this setting , the meaning comes down to the same thing. However, to watch generally means to look at something very actively. To see, simply means that you look at something and notice that it exists.

I would say that we use SEE when we do something unintentionally, when we open our eyes it is not a deliberate act, we see without any conscious effort. Watch is used when we look at something that moves or changes for a period of time. It is more a continuous action of looking and observing. In terms of a movie, you could use both, but I would suggest there is a slight difference. Generally we use SEE for public performances of something, and WATCH for television at home. We are going to see the latest movie at the cinema tonight. Last night I watched a great documentary on the television. Did you ever see Elvis Presley live in concert? We watched a good movie yesterday implies more that we watched it on the television. We saw a good movie yesterday would imply more that you did so by going to the cinema.

I would say that we use SEE when we do something unintentionally, when we open our eyes it is not a deliberate act, we see without any conscious effort. Watch is used when we look at something that moves or changes for a period of time. It is more a continuous action of looking and observing. In terms of a movie, you could use both, but I would suggest there is a slight difference. Generally we use SEE for public performances of something, and WATCH for television at home. We are going to see the latest movie at the cinema tonight. Last night I watched a great documentary on the television. Did you ever see Elvis Presley live in concert? We watched a good movie yesterday implies more that we watched it on the television. We saw a good movie yesterday would imply more that you did so by going to the cinema.